Comparisons of Morse and harmonic oscillator models for vibration-rotation excitation of H2 by Li+

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Abstract
Matrix elements of a potential for atom-diatomic molecule collision problems in three dimensions have been calculated using two models to describe the rotating-vibrating molecule. These models are the undistorted three dimensional harmonic oscillator model of Eastes and Secrest and a rotating-vibrating Morse oscillator. The most important difference between the two models is the presence of centrifugal stretching in the Morse oscillator model. A comparison of matrix elements is made which is applicable to any atom-diatom potential with a dependence on the vibrational coordinate in the form ξ, ξ2, eαξ, and ξeαξ. In addition, the specific example of Lester's ab initio Hartree-Fock potential for Li+–H2 is considered. Cross sections are calculated for Li+–H2 with limited basis sets for the harmonic and Morse oscillator at 0.1, 2.0, and 3.26 eV relative kinetic energy.